If there are genes "for jealousy", no one's found them yet, and no one can prove conclusively that they have found all of them, even if they've found some which are correlated with jealousy.

What I can tell you is this. There are areas of your brain that light up under MRI when you feel jealous. If you have a hole drilled in your head that takes out this part of your brain, you will probably stop feeling jealous; in fact, you will probably also stop feeling lots of other emotions that deal with social interactions and desire. Now, since the brain is an organ which constantly adapts to its surroundings, every time you feel jealousy, your brain is adapting to the way you react, and this could change the way you react to jealousy in general in the future. Exactly what changes would occur, I don't know, and wouldn't be able to predict. I think that's essentially the state of the field.

I imagine that personality is an extremely complex multifactorial set of traits; in other words, there's no "gene" for jealousy, but rather, a whole set of genes that are responsible for general personality and behavior. Then, you have to keep in mind that personality is also extremely variable based on environment and how the brain circuitry is "molded" by experience.